Hi!
Assume I create a sphere by
sphere=Sphere(Point(0,0,0),1)
and I then “discretize it” using
mesh=generate_mesh(sphere,16)
First Question: How to I control the size/access the size of the triangles (the “h”, so to speak).
Second Question: How do I define a function on the discretize sphere? Note, I am not interested in defining a function on the finite element space, but rather on the discretized sphere. In any regard…
I then want to, given a function defined on the discretized sphere, a f: \mathbb{S}_h^2 \to \mathbb{R} o be able to define a sort of “lifted” function defined on \mathbb{S}^2, where the lifted funtion is given by
where f^l(a), ~ a \in \mathbb{S}^2 is given by f(x(a)) where x(a)\in \mathbb{S}^2_h is the orthagonal projection of the point a to \mathbb{S}_h^2.
Third Question: How to do this?
Fourth Question: Given a function f defined on \mathbb{S}^2 , (which I define how? Tried to do using userexpression but failed), I wish to define a funtion f^{-l} on the discretized sphere given by a defining f^{-l}(x), ~ x \in \mathbb{S}_h^2 where x is the orthagonal extension of a a \in \mathbb{S}^2 . How do I do this?
Fifth Question (and final!): Can I “sample” a point from a sphere in fenics? or it’s discretization?